"""
Monte Carlo Tree Search (MCTS) implementation for mathematical reasoning
"""
from typing import List, Dict, Any, Optional, Tuple
import numpy as np
from dataclasses import dataclass
import json
from pathlib import Path

@dataclass
class MCTSConfig:
    exploration_weight: float = 1.0
    max_simulations: int = 1000
    max_depth: int = 10

class MCTSNode:
    def __init__(self, state: str, parent: Optional['MCTSNode'] = None, action: Optional[str] = None):
        self.state = state
        self.parent = parent
        self.action = action
        self.children: List[MCTSNode] = []
        self.visits = 0
        self.value = 0.0
        self.untried_actions: List[str] = []
        
    def add_child(self, action: str, state: str) -> 'MCTSNode':
        """Add a child node with the given action and state."""
        child = MCTSNode(state=state, parent=self, action=action)
        self.children.append(child)
        if action in self.untried_actions:
            self.untried_actions.remove(action)
        return child

    def update(self, reward: float) -> None:
        """Update node statistics with new reward."""
        if reward is None:
            reward = 0.0  # Default value for None reward
        self.visits += 1
        self.value += (reward - self.value) / self.visits
        
    def get_ucb_score(self, exploration_weight: float) -> float:
        """Calculate UCB1 score for this node."""
        if self.visits == 0:
            return float('inf')
        exploitation = self.value / self.visits
        exploration = exploration_weight * np.sqrt(2 * np.log(self.parent.visits) / self.visits)
        return exploitation + exploration

    def is_terminal(self) -> bool:
        """Check if this node represents a terminal state."""
        # Implementation depends on problem domain
        return False

    def get_possible_actions(self) -> List[str]:
        """Get list of possible actions from this state."""
        # Implementation depends on problem domain
        return []

class MCTS:
    def __init__(self, config: Optional[MCTSConfig] = None):
        self.config = config or MCTSConfig()
        
    @classmethod
    def from_config_file(cls, config_path: str) -> 'MCTS':
        """Create MCTS instance from config file."""
        with open(config_path, 'r') as f:
            config_data = json.load(f)
        config = MCTSConfig(**config_data['mcts'])
        return cls(config)
        
    def select_action(self, node: MCTSNode) -> Tuple[MCTSNode, str]:
        """Select the best child node using UCB1."""
        if not node.children:
            return node, ""
            
        ucb_scores = [
            child.get_ucb_score(self.config.exploration_weight)
            for child in node.children
        ]
        selected_child = node.children[np.argmax(ucb_scores)]
        return selected_child, selected_child.action
    
    def expand(self, node: MCTSNode) -> Tuple[MCTSNode, str]:
        """Expand the current node with a new child."""
        if not node.untried_actions:
            node.untried_actions = node.get_possible_actions()
            
        if not node.untried_actions:
            return node, ""
            
        action = np.random.choice(node.untried_actions)
        new_state = self.apply_action(node.state, action)
        child = node.add_child(action, new_state)
        return child, action
    
    def simulate(self, state: str, depth: int = 0) -> float:
        """Run a simulation from the current state."""
        if depth >= self.config.max_depth or self.is_terminal_state(state):
            return self.evaluate_state(state)
            
        actions = self.get_possible_actions(state)
        if not actions:
            return self.evaluate_state(state)
            
        action = np.random.choice(actions)
        new_state = self.apply_action(state, action)
        return self.simulate(new_state, depth + 1)
    
    def backpropagate(self, node: MCTSNode, reward: float) -> None:
        """Update the values up the tree."""
        while node is not None:
            node.update(reward)
            node = node.parent
            
    def search(self, root_state: str) -> Tuple[str, List[Dict[str, Any]]]:
        """Perform MCTS search to find the best action sequence."""
        root = MCTSNode(state=root_state)
        trajectory = []
        
        for _ in range(self.config.max_simulations):
            node = root
            
            # Selection
            while node.children and not node.untried_actions:
                node, action = self.select_action(node)
                trajectory.append({
                    "state": node.state,
                    "action": action,
                    "value": node.value,
                    "visits": node.visits
                })
                
            # Expansion
            if not node.is_terminal():
                node, action = self.expand(node)
                trajectory.append({
                    "state": node.state,
                    "action": action,
                    "value": node.value,
                    "visits": node.visits
                })
                
            # Simulation
            reward = self.simulate(node.state)
            
            # Backpropagation
            self.backpropagate(node, reward)
            
        # Return best action sequence
        if root.children:
            best_child = max(root.children, key=lambda c: c.visits)
            return best_child.action, trajectory
        else:
            # If no children were created, return a default action
            return "solve", trajectory
    
    def apply_action(self, state: str, action: str) -> str:
        """Apply an action to a state to get the next state."""
        # Simple default implementation for math problems
        return f"{state} -> {action}"
    
    def evaluate_state(self, state: str) -> float:
        """Evaluate the value of a terminal state."""
        # Simple heuristic based on state length/complexity
        return np.random.random()  # Random value between 0 and 1
    
    def is_terminal_state(self, state: str) -> bool:
        """Check if a state is terminal."""
        # Simple heuristic: consider longer chains as more likely terminal
        return len(state) > 100  # Arbitrary threshold
    
    def get_possible_actions(self, state: str) -> List[str]:
        """Get possible actions for a state."""
        # Simple default actions for math problems
        return ["step", "calculate", "simplify", "conclude"]
